# Small prismated tesseractic tetracomb

Small prismated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymSpittit
Coxeter diagramx4o3o3x4o ()
Elements
Tera6N tesseracts, 4N cuboctahedral prisms, N rectified tesseracts, N small disprismatotesseractihexadecachora
Cells16N tetrahedra, 32N triangular prisms, 4N+24N+24N cubes, 8N cuboctahedra
Faces64N triangles, 24N+24N+96N squares
Edges48N+96N
Vertices32N
Vertex figureTriangular antifastegium, edge lengths 1 (base edges of triangular prism) and 2 (all other edges)
Related polytopes
ArmySpittit
RegimentSpittit
ConjugateQuasiprismated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes

The small prismated tesseractic tetracomb or spittit, also called the runcinated tesseractic tetracomb is a convex uniform tetracomb. 1 rectified tesseract, 2 small disprismatotesseractihexadecachora, 3 tesseracts, and 3 cuboctahedral prisms join at each vertex of this tessellation. As the name suggests, it is the runcination of the tesseractic tetracomb.

## Vertex coordinates

The vertices of a small prismated tesseractic tetracomb of edge length 1 are given by all permutations of:

• ${\displaystyle \left(±\frac12+(1+\sqrt2)i,\,±\frac12+(1+\sqrt2)j,\,±\frac12+(1+\sqrt2)k,\,±\frac{1+\sqrt2}{2}+(1+\sqrt2)l\right),}$

Where i, j, k, and l range over the integers.

## Representations

A small prismated tesseractic tetracomb has the following Coxeter diagrams:

• x4o3o3x4o (full symmetry)
• x3o3x *b3o4x (half symmetry)

## Related polytopes

o4o3o3o4o truncations
Name OBSA CD diagram Picture
Tesseractic tetracomb test
Rectified tesseractic tetracomb rittit
Icositetrachoric tetracomb icot
Truncated tesseractic tetracomb tattit
Bitruncated tesseractic tetracomb batitit
Small rhombated tesseractic tetracomb srittit
Rectified icositetrachoric tetracomb ricot
Great rhombated tesseractic tetracomb grittit
Truncated icositetrachoric tetracomb ticot
Small prismated tesseractic tetracomb sidpitit
Prismatotruncated tesseractic tetracomb potatit
Prismatorhombated tesseractic tetracomb prittit
Great prismated tesseractic tetracomb gippittit
Tesseractic tetracomb test
Celliprismated tesseractic tetracomb capotat
Cellirhombated tesseractic tetracomb scartit
Celligreatorhombated tesseractic tetracomb gicartit
Celliprismatotruncated tesseractic tetracomb captatit
Great cellated tesseractic tetracomb otatit